High-energy Particle Transport Research Articles

Modeling the Transport of Nonthermal Particles in Flares Using Fokker–Planck Kinetic Theory

Abstract We describe a new approach for modeling the transport of high-energy particles accelerated during flares from the acceleration region in the solar corona until their eventual thermalization in the flare footpoint. Our technique numerically solves the Fokker–Planck equation and includes forces corresponding to Coulomb collisions in a flux loop with nonuniform ionization, synchrotron emission reaction, magnetic mirroring, and a return current electric field. Our solution to the Fokker–Planck equation includes second-order pitch angle and momentum diffusion. It is applicable to particles of arbitrary mass and charge. By tracking the collisions, we predict the bremsstrahlung produced as these particles interact with the ambient stellar atmosphere. This can be compared directly with observations and used to constrain the accelerated particle energy distribution. We have named our numerical code FP and distributed it for general use. We demonstrate its effectiveness in several test cases.

Transport of High-energy Charged Particles through Spatially Intermittent Turbulent Magnetic Fields

Abstract Identifying the sources of the highest energy cosmic rays requires understanding how they are deflected by the stochastic, spatially intermittent intergalactic magnetic field. Here we report measurements of energetic charged-particle propagation through a laser-produced magnetized plasma with these properties. We characterize the diffusive transport of the particles experimentally. The results show that the transport is diffusive and that, for the regime of interest for the highest energy cosmic rays, the diffusion coefficient is unaffected by the spatial intermittency of the magnetic field.

Diffusion in pulsar wind nebulae: an investigation using magnetohydrodynamic and particle transport models

We study the transport of high-energy particles in pulsar wind nebulae (PWN) using three-dimensional MHD (see Porth et al. (2014) for details) and test-particle simulations, as well as a Fokker-Planck particle transport model. The latter includes radiative and adiabatic losses, diffusion, and advection on the background flow of the simulated MHD nebula. By combining the models, the spatial evolution of flux and photon index of the X-ray synchrotron emission is modelled for the three nebulae G21.5-0.9, the inner regions of Vela, and 3C 58, thereby allowing us to derive governing parameters: the magnetic field strength, average flow velocity and spatial diffusion coefficient. For comparison, the nebulae are also modelled with the semi-analytic Kennel & Coroniti (1984) model but the Porth et al. (2014) model generally yields better fits to the observational data. We find that high velocity fluctuations in the turbulent nebula (downstream of the termination shock) give rise to efficient diffusive transport of particles, with average P\'eclet number close to unity, indicating that both advection and diffusion play an important role in particle transport. We find that the diffusive transport coefficient of the order of $\sim2\times 10^{27} (L_{\rm s}/0.42\rm Ly) cm^{2}s^{-1}$ ($L_{\rm s}$ is the size of the termination shock) is independent of energy up to extreme particle Lorentz factors of $\gamma_{p}\sim10^{10}$.

PENGEOM—A general-purpose geometry package for Monte Carlo simulation of radiation transport in material systems defined by quadric surfaces

The Fortran subroutine package pengeom provides a complete set of tools to handle quadric geometries in Monte Carlo simulations of radiation transport. The material structure where radiation propagates is assumed to consist of homogeneous bodies limited by quadric surfaces. The pengeom subroutines (a subset of the penelope code) track particles through the material structure, independently of the details of the physics models adopted to describe the interactions. Although these subroutines are designed for detailed simulations of photon and electron transport, where all individual interactions are simulated sequentially, they can also be used in mixed (class II) schemes for simulating the transport of high-energy charged particles, where the effect of soft interactions is described by the random-hinge method. The definition of the geometry and the details of the tracking algorithm are tailored to optimize simulation speed. The use of fuzzy quadric surfaces minimizes the impact of round-off errors. The provided software includes a Java graphical user interface for editing and debugging the geometry definition file and for visualizing the material structure. Images of the structure are generated by using the tracking subroutines and, hence, they describe the geometry actually passed to the simulation code. Program summaryProgram title: PengeomCatalogue identifier: AEYH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYH_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 89390No. of bytes in distributed program, including test data, etc.: 5062646Distribution format: tar.gzProgramming language: Fortran, Java.Computer: PC with Java Runtime Environment installed.Operating system: Windows, Linux.RAM: 210 MiBClassification: 21.1, 14.Nature of problem: The Fortran subroutines perform all geometry operations in Monte Carlo simulations of radiation transport with arbitrary interaction models. They track particles through material systems consisting of homogeneous bodies limited by quadric surfaces. Particles are moved in steps (free flights) of a given length, which is dictated by the simulation program, and are halted when they cross an interface between media of different compositions or when they enter selected bodies.Solution method: The pengeom subroutines are tailored to optimize simulation speed and accuracy. Fast tracking is accomplished by the use of quadric surfaces, which facilitate the calculation of ray intersections, and of modules (connected volumes limited by quadric surfaces) organized in a hierarchical structure. Optimal accuracy is obtained by considering fuzzy surfaces, with the aid of a simple algorithm that keeps control of multiple intersections of a ray and a surface. The Java GUI PenGeomJar provides a geometry toolbox; it allows building and debugging the geometry definition file, as well as visualizing the resulting geometry in two and three dimensions.Restrictions: By default pengeom can handle systems with up to 5000 bodies and 10,000 surfaces. These numbers can be increased by editing the Fortran source file.Unusual features: All geometrical operations are performed internally. The connection between the steering main program and the tracking routines is through a Fortran module, which contains the state variables of the transported particle, and the input-output arguments of the subroutine step. Rendering of two- and three-dimensional images is performed by using the pengeom subroutines, so that displayed images correspond to the definitions passed to the simulation program.Additional comments: Java editor and viewer (PenGeomJar), geometry examples, translator to POV-Ray™ format, detailed manual. The Fortran subroutine package pengeom is part of the penelope code system [1].Running time: The running time much depends on the complexity of the material system. The most complicated example provided, phantom, an anthropomorphic phantom, has 264 surfaces and 169 bodies and modules, with different levels of grouping; the largest module contains 51 daughters. The rendering of a 3D image of phantom with 1680x1050 pixels takes about 25 s (i.e., about 1.5⋅10−5 seconds per ray) on an Intel Core I7-3520M CPU, with Windows 7 and subroutines compiled with gfortran.

Design of a Heavy Liquid Metal Neutron Spallation Target for Experimental Accelerator driven Sub-critical Reactor

In this paper detailed design of a liquid metal Lead-Bismuth-Eutectic (LBE) neutron spallation target for an experimental ADS reactor of ~30 MW with sub-criticality (k) of 0.975 is presented. The high energy beam consists of 650 MeV and 0.9 mA proton beam. The circulation of the liquid metal is based on gas lift method. Extensive numerical simulations have been carried out to optimise the target geometry, LBE/gas flow rate, beam parameters, neutron yield etc. This paper also includes time dependent two phase CFD analysis to study the effect of nitrogen gas flow rate on LBE flow rate, 3D thermal-hydraulic studies of liquid metal flow near the window and spallation region. The optimum asymmetric flow geometry at the bottom of the target to shift the stagnation zone to minimize the window temperature and estimation of thermo mechanical stress in the window has been carried out. In addition, spallation neutron generation and their energy spectrum, heat deposition distribution, spallation products and their activities have been estimated using high energy particle transport code FLUKA.

A GAMOS plug-in for GEANT4 based Monte Carlo simulation of radiation-induced light transport in biological media

We describe a tissue optics plug-in that interfaces with the GEANT4/GAMOS Monte Carlo (MC) architecture, providing a means of simulating radiation-induced light transport in biological media for the first time. Specifically, we focus on the simulation of light transport due to the Čerenkov effect (light emission from charged particle’s traveling faster than the local speed of light in a given medium), a phenomenon which requires accurate modeling of both the high energy particle and subsequent optical photon transport, a dynamic coupled process that is not well-described by any current MC framework. The results of validation simulations show excellent agreement with currently employed biomedical optics MC codes, [i.e., Monte Carlo for Multi-Layered media (MCML), Mesh-based Monte Carlo (MMC), and diffusion theory], and examples relevant to recent studies into detection of Čerenkov light from an external radiation beam or radionuclide are presented. While the work presented within this paper focuses on radiation-induced light transport, the core features and robust flexibility of the plug-in modified package make it also extensible to more conventional biomedical optics simulations. The plug-in, user guide, example files, as well as the necessary files to reproduce the validation simulations described within this paper are available online at http://www.dartmouth.edu/optmed/research-projects/monte-carlo-software.

Particle transport in intense small-scale magnetic turbulence with a mean field

Various astrophysical studies have motivated the investigation of the transport of high energy particles in magnetic turbulence, either in the source or en route to the observation sites. For strong turbulence and large rigidity, the pitch-angle scattering rate is governed by a simple law involving a mean free path that increases proportionally to the square of the particle energy. In this paper, we show that perpendicular diffusion deviates from this behavior in the presence of a mean field. We propose an exact theoretical derivation of the diffusion coefficients and show that a mean field significantly changes the transverse diffusion even in the presence of a stronger turbulent field. In particular, the transverse diffusion coefficient is shown to reach a finite value at large rigidity instead of increasing proportionally to the square of the particle energy. Our theoretical derivation is corroborated by a dedicated Monte Carlo simulation. We briefly discuss several possible applications in astrophysics.

Shielding Experiments at High Energy Accelerators of Fermilab (IV) —Calculation Analyses—

JASMIN - Japanese and American Study of Muon Interaction and Neutron detection - a program for studies of shielding and irradiation effect around high energy accelerators has been started until 2007 using high energy proton accelerators located in Fermi National Accelerator Laboratory (FNAL) as a collaboration of JAPAN and FNAL. The series of the presentations entitled Shielding experiments at high energy accelerators of Fermilab describes the part of the results of this collaboration regarding transport of secondary particles, neutron and muon, from 120 GeV proton induced reactions through experimental data and simulation. In this paper, calculation analyses using high energy particle transport Monte Carlo calculation codes, PHITS, MARS and MCNPX, for the experiments carried out at the anti-proton production target station were performed with a simplified two-dimensional geometry to validate the accuracy of spatial distribution of reaction rate in iron shield and the attenuation length. The calculation results were good agreement with the obtained experimental data for the spatial distribution. Neutron attenuation lengths of iron were also given by the data. Tendencies of the attenuation length of iron were found the PHITS and MARS values were larger and the MCNPX values were smaller than the data.

COMBINED MODELING OF ACCELERATION, TRANSPORT, AND HYDRODYNAMIC RESPONSE IN SOLAR FLARES. I. THE NUMERICAL MODEL

Acceleration and transport of high-energy particles and fluid dynamics of atmospheric plasma are interrelated aspects of solar flares, but for convenience and simplicity they were artificially separated in the past. We present here self-consistently combined Fokker-Planck modeling of particles and hydrodynamic simulation of flare plasma. Energetic electrons are modeled with the Stanford unified code of acceleration, transport, and radiation, while plasma is modeled with the Naval Research Laboratory flux tube code. We calculated the collisional heating rate directly from the particle transport code, which is more accurate than those in previous studies based on approximate analytical solutions. We repeated the simulation of Mariska et al. with an injection of power law, downward-beamed electrons using the new heating rate. For this case, a ~10% difference was found from their old result. We also used a more realistic spectrum of injected electrons provided by the stochastic acceleration model, which has a smooth transition from a quasi-thermal background at low energies to a nonthermal tail at high energies. The inclusion of low-energy electrons results in relatively more heating in the corona (versus chromosphere) and thus a larger downward heat conduction flux. The interplay of electron heating, conduction, and radiative loss leads to stronger chromospheric evaporation than obtained in previous studies, which had a deficit in low-energy electrons due to an arbitrarily assumed low-energy cutoff. The energy and spatial distributions of energetic electrons and bremsstrahlung photons bear signatures of the changing density distribution caused by chromospheric evaporation. In particular, the density jump at the evaporation front gives rise to enhanced emission, which, in principle, can be imaged by X-ray telescopes. This model can be applied to investigate a variety of high-energy processes in solar, space, and astrophysical plasmas.

Fragmentation Calculations for Energetic Ions in Candidate Space Radiation Shielding Materials

Calculations have been carried out to evaluate the effectiveness of a range of carbon- and hydrogen-rich materials for shielding against energetic heavy ions relevant to the galactic cosmic ray spectrum. Experimental work integrated with the calculations included both preparation and characterization of physical properties of candidate materials and measurements of fragmentation (breakup) of ion beams of 16O and 40Ar in the tens of GeV energy range in these materials. We have simulated the fragmentation experiments using both the HETC-HEDS and PHITS high-energy particle transport codes. The purposes of these computational simulations were to investigate the effectiveness as spacecraft personnel shielding of various novel as well as commercially available materials for future lunar and interplanetary missions and to validate the codes against experimental data. In the present contribution we report results of the fragmentation simulations and compare them with examples of the experimental measurements.

High energy particle transport in stochastic magnetic fields in the solar corona

Aims. We study energetic particle transport in the solar corona in the presence of magnetic fluctuations by analyzing the motion of protons injected at the center of a model coronal loop. Methods. We set up a numerical realization of magnetic turbulence, in which the magnetic fluctuations are represented by a Fourier expansion with random phases. We perform test particle simulations by varying the turbulence correlation length λ, the turbulence level, and the proton energy. Coulomb collisions are neglected. Results. For large A, the ratio ρ/λ (with ρ the Larmor radius) is small, and the magnetic moment is conserved. In this case, a fraction of the injected protons, which grow with the fluctuation level, are trapped at the top of the magnetic loop, near the injection region, by magnetic mirroring due to the magnetic fluctuations. The rest of the protons propagate freely along B, corresponding to nearly ballistic transport. Decreasing A, that is, increasing the ratio ρ/λ, the magnetic moment is no longer well conserved, and pitch angle diffusion progressively sets in. Pitch angle diffusion leads to a decrease in the trapped population and progressively changes proton transport from ballistic to superdiffusive, and finally, for small λ, to diffusive. Conclusions. Particle mirroring by magnetic turbulence makes for compact trapping regions. The particle dynamics inside the magnetic loop is non-Gaussian and the statistical description of transport properties requires the use of such ideas as the Levy random walk.

Radiation Shielding Analysis for Various Materials in the Extreme Jovian Environment

ABSTRACTEarlier particle experiments in the 1970s on Pioneer-10 and -11 and Voyager-1 and -2 provided Jupiter flyby particle data, which were used by Divine and Garrett to develop the first Jupiter trapped radiation environment model. This model was used to establish a baseline radiation effects design limit for the Galileo onboard electronics. Recently, Garrett et al. have developed an updated Galileo Interim Radiation Environment (GIRE) model based on Galileo electron data. In this paper, the GIRE model was utilized to generate trapped proton and electron spectra as a function of Rj (Rj = radius of Jupiter = ∼71,400 km). Using these spectra and a high-energy particle transport codes (MCNPX and HZETRN), radiation exposures and dose effects for a variety of shielding materials (Al, polyethylene [PE], and Ta plus several other elemental materials for “Graded-Z” portion of the paper) and thicknesses are presented for the Icy Moon, Europa, Ganymede, and Callisto for several orbital inclinations. In addition, an in-depth discussion and absorbed dose calculations are presented for “Graded-Z” materials and several computer codes were utilized for comparison purposes. We find overall there is generally quite good agreement between the various computer codes utilized in the study: MCNPX (Monte Carlo) vs. HZETRN (deterministic) for slab shielding and the comparison of “Graded-Z” shielding using the CEPXS, NOVICE, and NASA JPL codes. Finally, we conclude that the merits of using “Graded-Z” materials that include PE, due to cost and weight, should aid future Jupiter mission planners and spacecraft designers.

A space radiation shielding model of the Martian radiation environment experiment (MARIE)

The 2001 Mars Odyssey spacecraft was launched towards Mars on April 7, 2001. Onboard the spacecraft is the Martian radiation environment experiment (MARIE), which is designed to measure the background radiation environment due to galactic cosmic rays (GCR) and solar protons in the 20–500 MeV/n energy range. We present an approach for developing a space radiation-shielding model of the spacecraft that includes the MARIE instrument in the current mapping phase orientation. A discussion is presented describing the development and methodology used to construct the shielding model. For a given GCR model environment, using the current MARIE shielding model and the high-energy particle transport codes, dose rate values are compared with MARIE measurements during the early mapping phase in Mars orbit. The results show good agreement between the model calculations and the MARIE measurements as presented for the March 2002 dataset.

Development of General-Purpose Particle and Heavy Ion Transport Monte Carlo Code

The high-energy particle transport code NMTC/JAM, which has been developed at JAERI, was improved for the high-energy heavy ion transport calculation by incorporating the JQMD code, the SPAR code and the Shen formula. The new NMTC/JAM named PHITS (Particle and Heavy-Ion Transport code System) is the first general-purpose heavy ion transport Monte Carlo code over the incident energies from several MeV/nucleon to several GeV/nucleon.

QMD and JAM Calculations for High Energy Nucleon-Nucleus Collisions

We describe the two simulation codes, QMD and JAM, for high energy nuclear reactions. QMD can treat the nucleus-nucleus reactions as well as nucleon-nucleus reactions based on the molecular dynamics. We have applied the QMD code intensively to nucleon-nucleus reactions and checked its validity. The cross sections obtained by the QMD are now used for evaluation of high energy nuclear data in JAERI. JAM is a hadronic cascade code including the resonance and string model for the hadron-hadron collisions at high energy up to 200 GeV. We have developed a high energy particle transport code NMTC/JAM by including the JAM code for the intra-nuclear cascade part.

High-energy particle transport code NMTC/JAM

We have developed a high-energy particle transport code NMTC/JAM, which is an upgraded version of NMTC/JAERI97. The applicable energy range of NMTC/JAM is extended in principle up to 200 GeV for nucleons and mesons by introducing the high-energy nuclear reaction code JAM for the intra-nuclear cascade part. We compare the calculations by NMTC/JAM code with the experimental data of thin and thick targets for proton-induced reactions up to several tens of GeV. The results of the NMTC/JAM code show excellent agreement with the experimental data.

Three-dimensional Fokker–Planck equation for trapped fast ions in a Tokamak with weak toroidal field ripples

The five-dimensional (5D) drift kinetic Fokker–Planck equation for fast charged particles confined in a tokamak with a toroidal field (TF) ripple magnitude below the Goldston–White–Boozer stochasticity threshold is averaged over the banana and superbanana timescales. As a result, a three-dimensional (3D) Fokker–Planck equation in the constants of motion (COM) space describing the collisional transport of charged high-energy particles is obtained. Toroidally trapped particles with the toroidal precession being in resonance with the ripple perturbations are shown to yield the main contribution to the ripple induced transport. It is found that the rates of ripple superbanana diffusion and convection in the radial coordinate significantly exceed the corresponding rates of the bananas in the axisymmetric limit. The superbanana diffusion and convection shown to be dominant in the MeV energy range may be responsible for the loss of partially thermalized fusion products observed in the Tokamak fusion test reactor (TFTR) [S. J. Zweben, R. L. Boivin, C.-S. Chang et al., Nucl. Fusion 31, 2219 (1991); H. W. Herrmann, S. J. Zweben, D. S. Darrow et al., ibid. 37, 1437 (1997)].

SADCO-2: a modular code system for generating coupled nuclear data libraries to provide high-energy particle transport calculation by multigroup methods

Abstract A system to produce coupled multigroup cross sections for providing calculations by multigroup methods over a wide range of energy for neutron, proton, pion, kaon, photon transport through matter has been developed. The main modules of the system as well as the SADCO-2 structure are described. The SADCO-2 nuclear data system is available from the Institute for High Energy Physics.

Beam heating and cooling of thick targets for on-line production of exotic nuclei

Calculations have been made of energy deposition distributions for “thick” targets (∼1 mole/cm 2) employed in on-line production of exotic nuclei using the Monte Carlo based LAHET code system for high-energy charged particle transport. A variety of target materials and incident proton beam energies have been examined. For 600 MeV protons, the results are compared to those from a similar study reported in the literature. The agreement between the two studies for total energy deposition is reasonably good for monatomic targets, but the results differ in some details of the energy deposition distributions. Target cooling, both radiative and conductive, is examined to assess the suitability of existing target concepts exposed to bombardment by intense (up to 100 μA), energetic (500 MeV to 1.2 GeV) proton beams to produce exotic nuclei. Implications of cooling requirements to target material selection and design are discussed.

Secondary particle yield and energy release data from intranuclear-cascade-evaporation model calculations of high energy (20–1100 MeV) neutron interaction with elements of shielding and biological importance

Secondary particle (neutron, proton, pion and heavy ion) yields and energy release data for 20, 50, 100, 300, 500, 800 and 1100 MeV neutron collisions with H, C, N, O, Al, Si, Ca, Fe and Pb have been calculated using the intranuclear-cascade-evaporation model. The low-energy limit is discussed and compared with the ENDF/B-IV neutron data. The mean elastic recoil energies have also been estimated by means of the Ranft formula for angular distribution. The multigroup response functions (kerma factors and production cross-sections) have been obtained and applied calculating the energy deposition and particle yields in the deep-penetrated graphite and iron spheres. The results for energy deposition of the ANISN neutron transport code using a high energy cross-section library and the derived kermas are about 10% overestimated relative to the thick-target results from the high energy particle transport code HETC. In the neutron transport discrete ordinates calculation the secondary production is underestimated when comparing with the HETC code.